Frequency-Domain Techniques for Tissue Spectroscopy and Imaging
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Chapter 7 Frequency-domain techniques for tissue spectroscopy and imaging S. Fantini and M. A. Franceschini Bioengineering Center, Dept. of Electrical Engineering and Computer Science, Tufts University, 4 Colby Street, Medford, MA 02155 Contents 7.1 Introduction 7.2 Instrumentation, modulation methods, and signal detection 7.2.1 Lasers and arc lamps 7.2.2 Pulsed sources 7.2.3 Laser diodes and light emitting diodes (LED’s) 7.2.4 Optical detectors 7.2.5 Heterodyne detection, digital signal processing, and Fourier filtering 7.2.6 A frequency-domain tissue spectrometer 7.3 Modeling light propagation in scattering media 7.3.1 The Boltzmann transport equation (BTE) 7.3.2 Expansion of the Boltzmann equation in spherical harmonics 7.3.3 The PN approximation 7.3.4 The P1 approximation 7.3.5 The reduced scattering coefficient 7.3.6 The P1 equation and the standard diffusion equation (SDE) 7.3.7 Solution of the standard diffusion equation in the frequency-domain 7.4 Tissue spectroscopy and oximetry 7.4.1 Optical properties of biological tissue 7.4.1.1 Absorption 7.4.1.2 Scattering 7.4.2 Absorption spectroscopy of tissues 7.4.3 Near-infrared tissue oximetry 7.4.4 Measurements of optical scattering in tissues 7.5 Optical imaging of tissues 7.5.1 General concepts 7.5.2 Non-invasive optical imaging of the human brain 7.5.2.1 Detection of intracranial hematomas 7.5.2.2 Functional imaging of the brain 7.5.3 Optical mammography 7.6 Future directions 1 7.1 Introduction In frequency-domain spectroscopy, the intensity of the light source is sinusoidally modulated at a frequency f. One can fully describe the modulated intensity using three parameters, namely the average intensity (DC intensity), the amplitude of the intensity oscillations (AC amplitude), and the phase (F) of the intensity wave. The modulation is defined by the ratio AC/DC. Because the phase measurement and the intensity modulation are the key features of frequency-domain spectroscopy, the term phase-modulation is sometimes used interchangeably with frequency-domain. The phase measurement is related to the time-delay experienced by the probing intensity-wave. If t is a typical time delay, the phase is of the order of wt, where w = 2pf is the angular modulation frequency. To obtain phase measurements with good signal-to-noise ratio, it is required that wt ~ 1, which is the condition that guides the choice of the modulation frequency, f. In the case of near-infrared spectroscopy and imaging of tissues, t ~ 1 ns for source-detector separations on the order of a few centimeters.1,2 Consequently, the condition wt ~ 1 determines f ~ 100 MHz, which falls within the radio-frequency range. The 100 MHz frequency range is the one typically used for frequency-domain optical studies of biological tissues. In this chapter, we describe the frequency-domain instrumentation (section 7.2), the theoretical modeling of light propagation in tissue (section 7.3), and in vivo applications of frequency-domain spectroscopy (section 7.4) and imaging (section 7.5). We have tried to make this chapter self-contained, while providing extensive reference to the literature as a guide for additional reading and for in depth coverage of topics that are only briefly mentioned here due to space considerations. 7.2 Instrumentation, modulation methods, and signal detection Frequency-domain spectroscopy can be implemented using several instrumental schemes. For instance, homodyne techniques [in phase-quadrature (IQ), or zero- cross detection] perform amplitude and phase measurements without down- converting the radio frequency, while heterodyne detection (using two oscillators) relies on down conversion of the radio frequency from the 100 MHz range to the kHz range. Furthermore, signal processing may involve zero crossing detectors and analog filters, or analog-to-digital conversion and Fourier filters. A comprehensive review of the instrumentation for optical studies of tissue in the frequency-domain can be found in Ref. 3. In sections 7.2.1-7.2.5, we describe the various light sources and modulation methods, and the principles of heterodyne detection with digital signal processing and Fourier filtering. In section 7.2.6, we describe a specific frequency-domain instrument for near- infrared tissue spectroscopy. 2 7.2.1 Lasers and arc lamps The emission of continuous-wave lasers and arc lamps can be modulated using devices based on the electro-optical (Pockels cells)4 or acousto-optical5,6 effect. A Pockels cell is a birefringent crystal whose indices of refraction can be varied by applying an electric field. The application of a time-varying voltage to the Pockels cell modulates the relative phase delay of the light components polarized along the two principal axes of the cell. If this relative phase delay, or retardation, oscillates between 0 and p, when the modulated Pockels cell is sandwiched between two crossed linear polarizers, each at an angle of 45° with respect to the principal axes of the cell, one achieves an intensity modulator. In fact, no light is transmitted when the retardation is 0, while all light is transmitted when the retardation is p. An acousto-optic modulator is a material that uses the piezoelectric and the photo-elastic effects to convert an oscillating electric field into mechanical vibrations, which in turn induce a spatially dependent index of refraction. When a standing acoustic wave is established, the acousto-optic crystal behaves as an oscillating refractive index grating that modulates the transmitted light by time-varying diffraction. Both electro-optic and acousto- optic devices require the light beam to be collimated. In the case of arc lamps, appropriate collimation optics are required. Pockels cells provide effective modulations up to about 500 MHz, and acousto-optic modulators up to about 300 MHz. The wavelength of the laser is chosen on the basis of the requirements of the particular application (absorption band of a chromophore, optimal penetration depth in tissues, etc.). Examples of externally modulated CW lasers suitable for optical studies of tissues include the krypton ion (647 nm) and He-Ne (633 nm) lasers. Dye lasers pumped by either argon or krypton lasers afford continuous tunability over a wide spectral range that covers the whole visible band. Arc lamps (Xe, Xe-Hg, etc.) provide continuous spectral emission from the UV (230 nm) to the near-infrared (1100 nm). Therefore, they are ideal sources for spectroscopic studies when a wide and continuous spectral range is required. 7.2.2 Pulsed sources It is possible to achieve a large modulation bandwidth by exploiting the harmonic content of pulsed sources with high repetition rates. These sources can be either mode-locked pulsed lasers (Nd:YAG, Ti:Sapphire, dye lasers, etc.)7 or synchrotron radiation.8,9 The repetition rate of the pulses gives the fundamental frequency, whereas the pulse width determines the width of the power spectrum band. The power spectrum of mode-locked lasers extends well above 10 GHz, an upper limit in frequency-domain spectroscopy imposed by the optical detectors rather than the light sources. The wavelengths of the above mentioned lasers are 1064 nm for the Nd:YAG, 660-1180 nm (tunable) for the Ti:Sapphire, and 625-780 nm (tunable) for dye lasers using DCM or oxanine 1 dyes. A 3 unique pulsed source is provided by synchrotron radiation, which continuously covers the UV/visible/near-infrared spectrum. 7.2.3 Laser diodes and light emitting diodes (LED's) Semiconductor lasers and LED’s can be intensity modulated by driving them with an oscillating current. As a result of the relatively fast response time of laser diodes, they can be modulated at frequencies up to the GHz range. The LED's modulation frequency bandwidth is typically limited to 150 MHz, and they emit light over a spectral bandwidth of about 50-80 nm. Consequently, LED’s can be used to measure continuous spectra.10 For frequency-domain tissue spectroscopy, one can find a number of laser diodes and LED's emitting in the wavelength region of interest extending from 600 to 1300 nm. Laser diodes are the most commonly used light sources in frequency-domain optical studies of tissue because of their cost-effectiveness, ease of modulation, and effective coupling to fiber optics, in addition to the fact that tissue spectroscopy can be effectively performed using a few discrete wavelengths (see sections 7.4.2 and 7.4.3). 7.2.4 Optical detectors Optical detectors employed in frequency-domain spectroscopy include photomultiplier tubes (PMT's),11-14 microchannel plate photomultipliers (MCP-PMT),15,16 avalanche photodiodes (APD),17,18 and charge coupled device (CCD) cameras in conjunction with a gated image intensifier.19,20 In all cases, the down conversion from the source modulation frequency f to the cross-correlation frequency Df (see section 7.2.5) can occur either internally to the detector, by modulating the detector gain at frequency f + Df, or externally by electronically mixing the detector output at frequency f with the down conversion signal at frequency f + Df. Photomultiplier tubes are very sensitive detectors. The cathode sensitivity is typically 50 mA/W, and a current amplification by about 107 determines an anode sensitivity as high as 1 A/mW. PMT’s can operate in the visible and in the near-infrared up to about 1,000 nm. For internal down- conversion, their gain is modulated by a signal applied to the second dynode of the amplification chain. The typical rise time of a PMT, which is in the nanosecond range, allows for a modulation bandwidth of several hundred megahertz. The faster response of microchannel plates makes them suitable devices for modulation frequencies of up to several gigahertz.